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Geometry of (p, f)-bienergy variations between Riemannian manifolds

Ahmed Mohammed Cherif|Embarka Remli
경북대학교 자연과학대학 수학과|2023.06|Kyungpook Mathematical Journal|제63권 제2호|pp. 251-261|DOI 10.5666/KMJ.2023.63.2.251

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키워드

p-biharmonic mapsp-harmonic mapsLiouville type theorems
주제분류수학

초록

In this paper, we extend the definition of the Jacobi operator of smooth maps, and biharmonic maps via the variation of bienergy between two Riemannian manifolds. We construct an example of (p, f)-biharmonic non (p, f)-harmonic map. We also prove some Liouville type theorems for (p, f)-biharmonic maps

Abstract

In this paper, we extend the definition of the Jacobi operator of smooth maps, and biharmonic maps via the variation of bienergy between two Riemannian manifolds. We construct an example of (p, f)-biharmonic non (p, f)-harmonic map. We also prove some Liouville type theorems for (p, f)-biharmonic maps

참고문헌 (14)

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  4. N. Course, "f-harmonic maps which map the boundary of the domain to one point in the target", New York J. Math, 13, pp.423~435 (2007)
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  7. A. Fardoun, "On equivariant p-harmonic maps", Ann. Inst. Henri. Poincare, 15, pp.25~72 (1998)
  8. G. Y. Jiang, "2-harmonic maps and their first and second variational formulas", Chinese Ann. Math. Ser. A, 7(4), pp.389~402 (1986)
  9. J. Liu, "Liouville-type Theorems of p-harmonic Maps with free Boundary Values", Hi-roshima Math, 40, pp.333~342 (2010)
  10. A. Mohammed Cherif, "On the p-harmonic and p-biharmonic maps", J. Geom, 109, pp.11~ (2018)
  11. D. J. Moon, "Liouville type theorems for p-harmonic maps", J. Math. Anal. Appl, 342, pp.354~360 (2008)
  12. N. Nakauchi, "A Liouville type theorem for p-harmonic maps", Osaka J. Math, 35, pp.303~312 (1998)
  13. S. Ouakkas, "On the f-harmonic and f-biharmonic maps", J. P. Journal of Geom. and Top, 10(1), pp.11~27 (2010)
  14. Embarka Remli, "On the Generalized of p-harmonic and f-harmonic Maps", Kyungpook Mathematical Journal, 61(1), pp.169~179 (2021), 경북대학교 자연과학대학 수학과

관련 논문AI추천

Geometry of Energy and Bienergy Variations between Riemannian ManifoldsAhmed Mohamed Cherif, Mustapha Djaa경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호On the Generalized of p-harmonic and f-harmonic MapsAhmed Mohammed Cherif, Embarka Remli경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제1호Semi-conformal $L$-harmonic maps and Liouville type theoremAhmed Mohammed Cherif, Embarka Remli강원경기수학회 · 한국수학논문집2022 · 제30권 제1호New Methods of Construction for Biharmonic MapsAhmed Mohammed Cherif, Aicha Benkartab경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제1호Biharmonic Maps on Doubly Warped Product ManifoldsKhaldia Madani, Seddik Ouakkas경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호Some results on $p$-harmonic maps from gradient Ricci solitonsNguyen Dang Tuyen, Tran Nhat Minh대한수학회 · 대한수학회보2025 · 제62권 제6호

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